arXiv subjects
Publications and source records attributed to Renxing Li.
In this paper, we investigated the solvability of G-SVIEs under two cases: time-varying Lipschitz coefficients and integral-Lipschitz coefficients. Using the Picard iteration method, we established the existence and uniqueness of solutions to G-SVIEs under these two conditions. Additionally, we prove the continuity of the solution with respect to parameters in parameter-dependent G-SVIEs with Lipschitz coefficients.
In this paper, we study backward stochastic differential equations driven by G-Brownian motion where the generator has time-varying monotonicity with respect to y and Lipsitz property with respect to z. Through the Yosida approximation, we have proved the existence and uniqueness of the solutions to these equations.
In this paper, we define the squared G-Bessel process as the square of the modulus of a class of G-Brownian motions and establish that it is the unique solution to a stochastic differential equation. We then derive several path properties of the squared G-Bessel process, which are more profound in the capacity sense. Furthermore, we provide upper and lower bounds for the Laplace transform of the squared G-Bessel process. Finally, we prove that the time-space transformed squared G-Bessel process is a G'-CIR process.
Objective. Elevated intracranial pressure (ICP) is recognized as a biomarker of secondary brain injury, with a significant linear correlation observed between optic nerve sheath diameter (ONSD) and ICP. Frequent monitoring of ONSD could effectively support dynamic evaluation of ICP. However, ONSD measurement is heavily reliant on the operator's experience and skill, particularly in manually selecting the optimal frame from ultrasound sequences and measuring ONSD. Approach. This paper presents a novel method to automatically identify the optimal frame from video sequences for ONSD measurement by employing the Kernel Correlation Filter (KCF) tracking algorithm and Simple Linear Iterative Clustering (SLIC) segmentation algorithm. The optic nerve sheath is mapped and measured using a Gaussian Mixture Model (GMM) combined with a KL-divergence-based method. Results. When compared with the average measurements of two expert clinicians, the proposed method achieved a mean error, mean squared deviation, and intraclass correlation coefficient (ICC) of 0.04, 0.054, and 0.782, respectively. Significance. The findings suggest that this method provides highly accurate automated ONSD measurements, showing potential for clinical application.
In this paper, we introduce $ G $-Bessel processes for a class of $ d $-dimensional $ G $-Brownian motions. Under the condition of dimensionality $ d $, we obtain that the $ G $-Bessel process is the solution of the stochastic differential equation. Furthermore, under the stricter condition of dimensionality, we establish the existence and uniqueness of a solution of the stochastic differential equation governing the $ G $-Bessel process and prove the nonattainability of the origin for $ G $-Brownian motion.
Heterogeneous morphological features and data imbalance pose significant challenges in rare thyroid carcinoma classification using ultrasound imaging. To address this issue, we propose a novel multitask learning framework, Channel-Spatial Attention Synergy Network (CSASN), which integrates a dual-branch feature extractor - combining EfficientNet for local spatial encoding and ViT for global semantic modeling, with a cascaded channel-spatial attention refinement module. A residual multiscale classifier and dynamically weighted loss function further enhance classification stability and accuracy. Trained on a multicenter dataset comprising more than 2000 patients from four clinical institutions, our framework leverages a residual multiscale classifier and dynamically weighted loss function to enhance classification stability and accuracy. Extensive ablation studies demonstrate that each module contributes significantly to model performance, particularly in recognizing rare subtypes such as FTC and MTC carcinomas. Experimental results show that CSASN outperforms existing single-stream CNN or Transformer-based models, achieving a superior balance between precision and recall under class-imbalanced conditions. This framework provides a promising strategy for AI-assisted thyroid cancer diagnosis.
In this paper, we study the stochastic Volterra integral equation driven by $G$-Brownian motion ($G$-SVIE). The existence, uniqueness and two types of continuity of the solution to $G$-SVIE are obtained. Moreover, combining a new quasilinearization technique with the two-step approximation method, we establish the corresponding comparison theorem for a class of $G$-SVIEs. In particular, by means of this method, the classical assumptions on partial derivatives of the coefficients are unnecessary.
Background. Infectious diseases, particularly COVID-19, continue to be a significant global health issue. Although many countries have reduced or stopped large-scale testing measures, the detection of such diseases remains a propriety. Objective. This study aims to develop a novel, lightweight deep neural network for efficient, accurate, and cost-effective detection of COVID-19 using a nasal breathing audio data collected via smartphones. Methodology. Nasal breathing audio from 128 patients diagnosed with the Omicron variant was collected. Mel-Frequency Cepstral Coefficients (MFCCs), a widely used feature in speech and sound analysis, were employed for extracting important characteristics from the audio signals. Additional feature selection was performed using Random Forest (RF) and Principal Component Analysis (PCA) for dimensionality reduction. A Dense-ReLU-Dropout model was trained with K-fold cross-validation (K=3), and performance metrics like accuracy, precision, recall, and F1-score were used to evaluate the model. Results. The proposed model achieved 97% accuracy in detecting COVID-19 from nasal breathing sounds, outperforming state-of-the-art methods such as those by [23] and [13]. Our Dense-ReLU-Dropout model, using RF and PCA for feature selection, achieves high accuracy with greater computational efficiency compared to existing methods that require more complex models or larger datasets. Conclusion. The findings suggest that the proposed method holds significant potential for clinical implementation, advancing smartphone-based diagnostics in infectious diseases. The Dense-ReLU-Dropout model, combined with innovative feature processing techniques, offers a promising approach for efficient and accurate COVID-19 detection, showcasing the capabilities of mobile device-based diagnostics